Giuliani got it right. The president liked his performances. He got Cohen off the hook. Cohen paid off Stormy (and others) and Trump reimbursed him by means of monthly "retainer" payments. As Giuliani said, this is what fixers (and lawyers) do. It is not clear that Cohen did anything illegal, except hushing up Trump's involvement in a possible Federal Energy Commission violation (not reporting Trump's personal donation to the campaign).
The bottom line is that Giuliani gets Cohen off the hook, and show support for him. Admitting that Trump lied about the payment is really no big deal.
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The much bigger story is that Trump and Cohen won't tell the Trump's DC lawyers what was in the documents in Cohen's office. Also, Trump has gotten rid of the last of the old group of lawyers, and is preparing to fight Mueller and impeachment with his new lawyer who successfully defended Clinton.